Variable Step/Order Generalized Upwind Methods for the Numerical Solution of Second Order Singular Perturbation Problems

Keywords: Two-point Boundary Value Problems, singular perturbation problems, finite
difference schemes, upwind method, mesh variation.

Abstract: We propose a simple and quite efficient code to solve singular perturbation
problems when the perturbation parameter ? is very small. The code is based on generalized
upwind methods of order ranging from 4 to 10 and uses highly variable stepsize to fit the
boundary regions with relatively few points. An extensive numerical test section shows the
effectiveness of the proposed technique on linear problems.

 

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